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Thursday, February 19, 2009

Evidence for the Black Hole Event Horizon

Yesterday we had a very nice colloquium by Ramesh Narayan from Harvard

Evidence for the Black Hole Event Horizon

Abstract: Astronomers have discovered many candidate black holes in the universe and have studied their properties in ever-increasing detail. Over the last decade, a few groups have developed observational tests for the presence of event horizons in candidate black holes. The talk will discuss one of these tests, which indicates that the supermassive black hole at the center of our Galaxy must have a horizon.

Black hole formation is a prediction of General Relativity (GR). We know that stars that have masses more than a few times the solar mass can not, once their nuclear power is burned out, stabilize at a finite radius and the gravitational pressure of their own mass will cause them to completely collapse. In this process, the density of the object increases, and the gravitational force on the surface gets stronger. If the gravitational force on the surface gets so strong not even light can escape, we call this surface an event horizon. It is the characteristic feature of black holes. Classically, nothing can ever leave the region behind the event horizon.

Since the early 90s, evidence has mounted for astrophysical black holes. These come in two rough categories: solar size black holes, with masses of a few times the mass of our sun that form directly from collapse of stars, and the so-called supermassive black holes, with masses about a million to a billion times the solar mass, that form through accretion in densely populated areas, mostly in the center of galaxies.

The cheap way to label an object a black hole is to measure its mass (eg from the motions of nearby stars) and its radius (eg by determining the source area of its emission). For a black hole, we know the relation between both, R = 2 GM, where G is the gravitational constant, R is the radius, and M is the mass. The radius of a black hole of about solar mass would be roughly 3 km, and that of a supermassive black hole is then consequently some million to billion kms. If one has data that allows to estimate mass and radius, if there is too much mass in an observed region of spacetime, one can conclude it has to be a black hole. (Keep in mind this is astrophysics, so observables typically have large errorbars and it takes some effort to pin down conclusions.)

This is however somewhat unsatisfactory. What one would really like to know is whether the object does have an event horizon, which is the defining feature of a black hole. The question is then, what observables can help us to determine whether we are dealing with a compact object that has a surface, or with an object that has an event horizon?

First let me emphasize that compact objects of the masses we are concerned with here that have a radius close by but not quite the radius of a black hole are not possible in GR. These objects can't be stabilized. But if one modifies GR, one can get away with this. People have looked into such modifications but these are not very convincing options. The reason is simple: To avoid collapse, one needs a mechanism to stabilize matter at a density that allows the matter to just not form a black hole. That is, one needs a deviation from the standard theory at densities of about M/R3, and inserting the black hole radius this goes as ~ 1/M2. This means, the more massive the black hole is, the smaller is the density at which you need deviations from the standard theory.

And this density can be arbitrarily small. It can be as small as densities we deal with every day. Take a supermassive black hole with 109 times the mass of the sun, which has a radius of about 109km. This gives a density of about 1039kg per 1027km3, or 1 kg per dm3, which is about the density of water. Not exactly a very extreme condition, and one that we have quite some experience with. From Einstein's field equations we further know the density scales like the background curvature. This means if you want to generally avoid the formation of black holes, you need modifications of GR in the arbitrarily small curvature regime. In this regime, the theory is extremely well tested, and we have not seen any deviations whatsoever.

But still, one would like to have observational evidence for the presence of the horizon (after all, it could be a naked singularity, no?). The key to this is to compare the emissions of an object that does have a surface with that of an object that does not have a surface. Astrophysical black holes accrete matter, and that matter heats up, which leads to emissions. When the accreted matter hits the surface this also leads to emissions, that can - in the case of astrophysical black holes - be violent nuclear explosions. An object with an event horizon on the other hand will not have contributions to the emitted radiation from the surface. Both will thus differ in their luminosity, which is observable.

In his talk, Narayan summarized the observations of the luminosity of both solar mass black holes in our galaxy, and for Sgr A*, the supermassive black hole in the center of our galaxy. In both cases, the observed emission is much smaller than would be expected if the object had a surface, and thus clear evidence for the presence of an event horizon.

"First let me emphasize that compact objects of the masses we are concerned with here that have a radius close by but not quite the radius of a black hole are not possible in GR."

Yes! Hardly anyone ever points this out! Well done! :-)

Now for some idle thoughts. We often say that a black hole of solar mass would have a radius of 3km or so. But as you know of course, the r coordinate in Schwarzschild doesn't measure lengths. So strictly speaking what we should say is that a black hole of solar mass would have a surface area of 4pi x 9 km^2. In reality the geometry inside a very dense star won't be close to Euclidean, so the proper radius *won't* be 3 km. Of course, in agreement with your statement above, if we try to make the star too small then it will collapse anyway. But my question is: I wonder what is the *proper* volume of a star of solar mass that is about to collapse [with "reasonable" assumptions about the density and pressure....]? It would be fun if the volume turns out to be huge. I would call that a "Bag of Copper". Note to the unwary: I'm feeling sleepy, all this could be utter rubbish.

“This gives a density of about 1039kg per 1027km3, or 1 kg per dm3, which is about the density of water. Not exactly a very extreme condition, and one that we have quite some experience with.”

I’m sorry yet I must ask probably what amounts to being a stupid question, as I’m somewhat confused here. Does this mean that the Schwarzschild radius of such a super massive black hole would have at such radius the density of an object comparable to that of water? I would have thought that the critical density of such objects consistent regardless of size. So in short are you saying that the Schwarzschild radius doesn’t describe a consistent critical density? That is this density varies downward with a increase in size.

So to extrapolate this further, what would the radius for our universe be; given all observed and even theorized matter/energy considering it’s estimated current age. This would suggest that if all is considered this density of matter/energy at the universes Schwarzschild radius would be extremely low; like far less then air. I guess what puzzles me is to ask what force could then provoke a universe to be able to expand not just initially from a point yet from beyond this radius?

I’m sorry yet I must ask probably what amounts to being a stupid question, as I’m somewhat confused here. Does this mean that the Schwarzschild radius of such a super massive black hole would have at such radius the density of an object comparable to that of water? I would have thought that the critical density of such objects consistent regardless of size. So in short are you saying that the Schwarzschild radius doesn’t describe a consistent critical density? That is this density varies downward with a increase in size

Yes, that is exactly what I am saying. It is a very common misunderstanding, but black hole formation does *not* happen as a fixed (or large) density. It is only if you have very little mass available (like we have in practice in our labs) that you would need to squeeze it together to a very high density to form a black hole.

The universe expands roughly speaking because of its initial conditions. I don't know what the Schwarzschild radius of the universe is, but I am sure somebody has computed it. Best,

Yes, that is correct. Well, as you indicate that is more or less the story with the bag of gold monster we discussed earlier. If it is about to collapse, the proper volume should indeed be huge. I'd think it goes with g_rr and g_rr is roughly 1/(1-2M/r) which diverges as r->2M (I say roughly because this is the static solution). Best,

To distinguish between the surface and the horizon. In the presentation of course is to pinpoint two issues. I am only concerned with one.

I am not totally clear here, although I do have the lecture handy, it is to bad I could not see the displays he was referring too. Also I had a difficult time finding the right media player as it did not have sound using Microsoft media Or VLC. I finally was able to use a DIVX player which then allowed the sound to work. Maybe, just my machine.

The collapse of course then produces two different circumstances. The gas and the surface becomes confusing.

The "compressibility of the gas" is in relation to what the heat generated specific, as it relates to the viscosity, pointing toward a singularity of the blackhole. But by it's very nature, it is revealing "the demonstration of the jets" in the cosmological picture, from what I understood. But of course I could be wrong.

It is the relativistic nature while seeing such a collapse that the interpretation comes from realizing "there is an avoidance," as the jets reveal.

Thusly it is these ones that are giving perpetuity to the birth of our universe? These are defining the current state of the universe?:)

Now as I understand it if a measurement is made on a pure state it will be turned into a mixed state. Of course there is the question of what constitutes a measurement. But it sounded like from the paradox argument there can never be a mixed state. QM doesn't allow it. It seems to me the universe would be either all pure states or all mixed states depending on what constitutes a measurement.

GPS confirms time passes more slowly in a gravitational well than in an external observer's clock. Collapse a stellar core into a black hole. As local escape velocity approaches lightspeed local time as externally viewed asymptotically stops. There is no unlimited collapse (within the universe's lifetime).

The naked singularity needs a modest density to stay inflated - crushed past Fermi exclusion but stuck in time evolution of states.

I am not really sure what you are saying. That there can be matter that avoids hitting the singularity because of strong interactions in the infalling gas and subsequent possibly violent eruptions does not mean the formation of the singularity is avoided altogether. Best,

What is not allowed in QM is the evolution of pure states into mixed states. It does allow mixed states. The issue with the black hole evaporation is that it will produce a mixed state no matter what you started from. So you can chose to start with a pure state, will get a mixed state, and have a problem. Best,

“Yes, that is exactly what I am saying. It is a very common misunderstanding, but black hole formation does *not* happen as a fixed (or large) density.”

Thanks and I must say I’ve learned something that perhaps I should have known before. It shows one the difference between those who simply read about theory and those that actually carefully study theory along with solving the equations. When black hole formation is talked about it usually is described as the concentration of mass in a dying star where the force of gravity overcomes the nuclear forces resisting collapse. I really have to look at this more carefully. As I was speculating earlier this means that an extremely low and separated concentration of mass could result in the formation of a black hole if the expanse of mass is large enough. It’s also interesting to consider as to exactly how and to what extent the expansion of space offsets this potential. This has so many connotations, even questions concerning a non local nature if taken to extreme.

“The universe expands roughly speaking because of its initial conditions”

Yes of course, yet it is those initial conditions that are not understood. It would seem as if time would had to have run backward from the singularity to beyond what would be considered the event horizon and at that moment somehow reverse. It’s often suggested that inflation represents the period that spatial expansion is faster then light; couldn’t it also be looked at as an initial state where time runs backwards until a certain point. Then again what would cause such reversal? This event horizon seems to act like a censor of sorts, to limit knowledge rather then information. I would ask, what significance does this truly hold? I guess what I’m asking is in as the size of the horizon tells one the sum total of the entropy contained at any given external time of observation, what is the importance of the details beyond this? For instance, QM itself has an information limit built in, so then what is so remarkable if GR in certain circumstances (limit) exhibits something similar? It’s treated like all is lost, yet we can know its entropy along with its charge and angular momentum, which is often more then is known in respect to things at times in QM. As the saying goes “the devil is in the details”.

Just one more comment that is actually more central to the theme of your post, which is to wonder if Moffat’s grey star explanation under MOG would account for the same data? It would appear to me that it could and that rests with perhaps the then only discernible difference being the actual size of the horizon under standard GR and the size of the grey star which I suspect would be smaller. Of course I don’t know what this size would be since this was never quantitatively explained within Moffat’s book for such objects or even the regular stellar ones for that matter. I don’t want it to sound like I’m a broken record with this, it's simply if ever or whenever you decide to carefully assess Moffat’s proposal I would truly value your opinion and insights.

Just a short and of course unqualified reaction of my own, is to say that although deep down I like the removal of dark matter from cosmology consideration and the riddance of the need to account for dark energy as currently only in adjusting the cosmological constant, I find Moffat’s need to set carefully several other free parameters somewhat unsatisfying. I would speculate that if Einstein himself looked at this he may voice a similar complaint. Then of course I’m far from being any authority in such matters and this is just a personally take.

Hello BeePhils questions were very similar to questiones I asked (myself) since decades. He dared to ask, this encourages me to put another question in this context. In one answer, You wrote about the Schwarzschild radius of the universe, whether somone ever calculated its Schwarzschild radius. There is the question preventing me to sleep since years :=) :How big ever that radius might be,the universe should have been smaller at some stage shortly after big bang,right?Which would prevent the expansion, would it?Another question related (in my thoughts at least)Oscillating universes (Friedmann I suppose)have a certain renaissance shortly. What is the fate of a black hole between big crunch and new bang?I hope this questiones are not too silly!Georg

with initial conditions I didn't mean conditions at 'the first moment of time'. Initial conditions can be at any moment. Indeed, they can be in the past if you like. You are right that we don't know what happened in the 'first moments' since this is in a regime where classical GR breaks down. Best,

Yes, there is information getting out in the jets, but not all information. As long as there is matter that collapses and forms the black hole, there will be information connected with it. You'd have to claim that all matter is re-emitted in jets and the black hole never forms to circumvent that. Best,

B.

PS: In the usual studies of the black hole information loss problem it is assumed that the collapsing matter does not interact, thus no jets. Though unrealistic, it serves to sharpen the problem and avoids unnecessary clutter that is not relevant for the issue.

Hi Bee:Thanks for the reply but I am not sure I understand the answer. My question is simple: It the physical world how does a mixed state come about? Starting from a pure state you always get a pure unless...what??

Unless you perform a measurement or, if the system you are considering is not isolated, have decoherence. See, if you consider only a part of the whole system, the evolution in the whole system can be unitary, but in the part you are considering it generically will not. (This was one of the points we tried to get across in the recent paper: If the final state is not a description of the whole system you shouldn't be surprised if evolution seems non-unitary.) Best,

Both Phil and Georg see the entropic valuation of information that is getting out, but do not realize the significance of the "finer constituent" of the reality in those jets? So rotational or not?

That it can support the existing state of the universe, as well as define it entropically, as it sits today. I have to be careful that I might not suggest some Einstein Rosen bridge that is far from appealing here in today's work?

How shall such variances be struck that we may see the universe with different speeds in it's expansionary times, if we do not look for the sources of this contribution?

That Susskind and others found the relevance in relation to microscopic views, initiated in particle collisions, is to recognize the state of the industry and where it is going in our explanations.

We can look at current experimental situations according to the back drop of this new physics. One just had to know where to look, and then look back at the cosmos and see the cosmological events that are initiated? How they release this information

Look, I already told you earlier I didn't read John's book, so I do not feel qualified to judge on it.

In the above post I have explained why I consider such compact, stable, almost-black-hole scenarios extremely implausible. This accounts for grey stars or gravstars or dark energy stars or anything of that sort. I am not saying it is not possible. I am saying it is very implausible. And if you want to explain the data I wrote about in this post with these scenarios, it becomes even more implausible. If you want to get a sense of this, I recommend you watch the recording, because John was there in the talk, and he defended his theory (towards the end of the talk). In the end however, the only way out is to argue that Sgr A* is not in equilibrium with its environment, i.e. the whole area is in its current form very young. Now I am not an astrophysicist, and we unfortunately don't have data that could confirm these stars have been moving around something black-hole-like for some thousand years (or whatever timescale it takes for stars to approach equilibrium, I have no clue), but this too seems very implausible to me. Not to mention that this argument would have to be made for any black-hole-like object. Thus, the moment that we have sufficient data from other supermassive black hole, you will either have to argue all of them are 'just born' and not in equilibrium with their environment, or admit they are just black holes.

To be honest, it is a mystery to me why people have a problem with the black hole horizon. I can understand one can have issues with the singularity, but then that's where we can GR expect to break down anyway. But a horizon is nothing very extreme. It's just some surface in our spacetime that happens to have a specific meaning for the tipping of lightcones. Period. It is one of the most general predictions of General Relativity. People have tried in the early last century to find reasons why these solutions are merely theoretical and don't exist in reality, but they failed. Instead they proved these solutions are very general indeed. And now we have experimental evidence that has been mounting since two decades. I simply don't understand what it is good for bending and altering such a beautiful theory that is in agreement with the data so well just to get rid of of the horizon which is, as far as I am concerned, one of the most fascinating properties of our spacetime to begin with. Best,

For all we know our universe is open, this means the (spatial) volume is infinite. It is infinite, and it always was infinite. What people usually talk about when they speak about the expansion of the volume is they think of some unit of volume and trace its evolution in time. What they mean when they talk about the volume of the universe is the volume of the OBSERVABLE universe, which is finite, and this is what I was referring to.

Besides this, there is not generally a problem with matter being inside its own Schwarzschild radius, as long as there is no future event horizon, which depends on the initial conditions. If you have a singularity in the past you can instead have a past event horizon (this means you have a region of spacetime where nothing can ever go in, as in contrast to a future event horizon where nothing can ever come out.) Either way however, you have to take into account that the only way to understand the causal structure is to look at the solutions to Einstein's field equations. And the Schwarzschild solution is a vacuum solution, meaning there is is vacuum outside some (possibly shrinking) radius. It is just not a solution that applies for a homogeneously filled universe.

Not really expecting a definitive answer here, but was curious what I could learn:

As stated, one might find a naked singularity (though that may be just as implausible as a surface). I presume just as a surface looks different than a horizon, and the telltale signatures of each are anticipated, the appearance of a naked singularity is also taken into account when interpreting the data. What might such a thing look like from so far away?

“Look, I already told you earlier I didn't read John's book, so I do not feel qualified to judge on it.”

I must apologize as It seems that somehow I unintentionally ruffled some feathers. I would of course not expect that you would or should offer an opinion on Moffat’s proposal before you had thoroughly reviewed it. Also, as I said earlier the book in itself is not technical enough for the purpose and suspect only a review of the related papers would be sufficient. More so I didn’t suggest that you spend the time unless you had an interest in doing so. All I was genuinely interested in was your opinion and insights in the case that you ever do find reason to. Also thanks for informing me that at this meeting Moffat himself defended his theory in the wake of the new data and I will be sure to watch it with even greater interest.

As for having difficulty in accepting the reality of an event horizon, I have no such aversion and like you find this one of the most interesting consequence of GR. However, I see no problem with considering that GR is in some way incomplete (rather then simply wrong) for even its creator in the end had his own reservations.

I do on the other hand have a problem with dark matter and to a lesser degree dark energy, since they are more or less accepted as necessary in order to have GR remain untouched; rather then resultant of having any firm, that is meaning direct observational evidence or model of consensus as to what each of them are in any sense of detail or clarity. There is also the non even distribution of dark matter that is normally required to explain galactic rotational speed, that on the surface appears so unnatural, with little explanation as to why it should be this way.

In short I’m not saying I don’t think they exist, yet like those from Missouri I’d like to have it more convincingly shown that they do, as to be able to confidently embrace it. So if it be MACHOs, WIMPs, neutrinos or whatever, it would be nice if they be found, identified and be consistent with theory.

Do you remember me mentioning the incident of having two books, one in either hand? One of these books was Susskind's "Blackhole Wars," which I stopped by the library to pick up yesterday, and the other was called Symmetry by Leon M. Lederman and Christopher t. Hill.

Susskind "summarizes the state of the industry" and where they are at from my quick review. Correlated with the intro to th blackhole wars presented in the Cosmic landscape. This coincided with the research I've piecemeal together over the years and thought having seen this "correlation in thinking already," my selection of book "Symmetry" was the right one.

Not that I did not think less of Susskind's relation to the issues of Blackholes, or, was irrelevant, or that it was to costly at the time. It just was where one might go toward seeing the universe in the way one does. Elevate the thinking to a position our leaders in science may hold?

How shall one describe this entropic valuation? Sean Carroll( he talks a lot about arrow of time, Boltzman Brain). He looks at the WMAP and is looking at, in my perspective, for the answer as well in relation to how such a state of the universe can exist in the way it does. So what I presented to Bee here in this comment section is in relation to that perspective.

Susskind thought well of it to defend his perspective in relation to his book, The Cosmic Landscape and speak to the detractors of that stringy landscape. I could be wrong of course.

Stanley Mandelstam's work was progressive in this area by describing a evolving genus figure in one of those valleys.

Lee failed to realize that this was a continuing effort of abstraction, as to the state a universe could have reached. All kinds of innuendos as to the anthropic discussion, and it's relation too...Intelligent design... well I'd rather not get into it here.

So what does this have to do with quantum gravity?:) ON a most generalized level and cosmological interpolation, what information is being released? Symmetry breaking, or not?

The constituents of the universe are all there in "new physics" demonstrations? They "exist now," so how can this universe exclude those finer constituents while we are only "surmising an entropic valuation?" Contribution,to such a "state of the universe" in the way it is?

Who knows how one may interpret the "escape of the photon" in relation to interpreting the Lagrangian views realized in the three body problem? One's view of the universe can have be severely altered once grokking an assumption.:) Or like me, just plain wrong.:)

Perhaps I haven’t yet recognized that the paradigm has shifted, yet I do try to keep up as best I can. I think that Susskind is a little to anxious to usher out the old before the new have been proven to lend more insight. As an example I quote from the book of his you mention “The Black Hole Wars”:

“Confusion and disorientation reigns; cause and effect break down; certainty evaporates; all the old rules fail. That’s what happens when the dominant paradigm breaks down.

But then new patterns emerge. They make no sense at first, but they are patterns. What to do? Take the patterns and classify, quantify, and codify them in new mathematics, even new laws of logic, if necessary. Replace the old writing with new and become familiar with it. Familiarity breeds contempt, or at least acceptance.

Very likely we are still confused beginners with very wrong mental pictures, and ultimate reality remains far beyond our grasp. The old cartographer’s term terra incognito comes to mind. The more we discover, the less we seem to know. That’s physics in a nutshell.”

Well it seems that like many of Susskind’s stripe the beauty of the patterns holds greater power of persuasion then the measure(s) of truth upon which science is built. Although I would admit that when pushing frontiers science often finds itself at times in ‘terra incognito’, yet it has never considered forsaking ‘terra firma’ as a required sacrifice.

This talk was good. However there are still loopholes in the argument. The direct proof will mainly come from gravitational waves.

BTW one thing not so well known is that Einstein and Dirac had very strong issues against black holes. Seehere and hereAlso there has been a lot of work on nonsingular alternatives to black holes by Gliner, Dymnikova and others and this was first proposed by Sakharov.

I just wanted to thank you for pointing to Dr. Ramesh Narayan's PIRSA talk on the evidence for black hole horizons; which I finally got around to watching. I must say that with admittedly my limit of evaluation it seems pretty convincing. Also, until now I wasn’t aware that binary neutron star systems were responsible for some of the gamma ray bursts that have been observed. This I find as truly interesting as I never imagined such things caused by belching stars so to speak:-) With all this in consideration it appears Moffat’s position that black holes don’t exist has suffered a serious blow with this evidence. Then of course the existence of a singularity is still an open question.

Narayan’s lecture was not only informative yet I also enjoyed his enthusiasm and charisma. It’s nice to hear a physicist point to a result and refer to its conclusion as a “no brainer”. He certainly would be a benefit as a teacher for anyone.

I am glad you liked the talk. I too liked his energy and enthusiasm. It is rare to have a scientists publicly say things like something is a 'no brainer'. For usual they are more careful in adding qualifiers. Though I am not sure whether it's a good thing I am grateful he expressed it so clearly for I hope people finally stop wasting their time with constructing evasions from these observations. Best,